Singular value decompositions and applications. 

It covers the mathematics of SVD and its applications in image compression and information 
retrieval(Latent Semantic indexing). Image compression and information retrieval makes use 
of the truncation of singular values of matrix. The reference is the following:

1. Image compression: [http://fourier.eng.hmc.edu/e161/lectures/svdcompression.html]
2. Latent Semantic indexing: [http://en.wikipedia.org/wiki/Latent_semantic_analysi],
3. Proof: P.1-2 of hku math2303 lecture note chapter 5 prepared by Dr. N.K. Tsing.
   [http://cklixx.people.wm.edu/teaching/m2999-1b3.pdf]
4. SVD's relation to 4 fundamental subspace: P.2-3 of Gilbert strang's article
  "The Four Fundamental  Subspaces:4Lines"    [http://cklixx.people.wm.edu/teaching/m2999-1b4.pdf]
5. SVD-LSI tutorial from [www.miislita.com],
6. Berry, Dumais and OBrien: "Using Linear Algebra for Intelligent Information Retrieval"(1994)P.1-10.
      [http://cklixx.people.wm.edu/teaching/m2999-1b6.pdf]
7. Martin and Berry: "Mathematical Foundations Behind Latent Semantic Analysis" (2006)P.45,49
          [http://cklixx.people.wm.edu/teaching/m2999-1b7.pdf]